> but the way we _necessarily_ have to reduce it to lossy theories means that we can only ever approach it with a non-zero error.
Yes. Fortunately, we also usually don't need the error to be zero. In practice, we usually have narrow scope at any given time, and can get away with a lot of error.
E.g. people in the past found alternatives to modern germ theory, involving evil spirits and other such shenanigans, but to the extend they covered the high-level mechanisms (curse transfers through contact, hygiene and boiling water removes the harmful effects, etc.), it doesn't really matter the theories were wrong. The beliefs were consistent with each other and empirical evidence to some degree, and to that degree were useful.
> And a theory focusing on one aspect, minimizing representational error from one direction of approaching it, necessarily has to make assumptions that will contradict those made by another theory trying to minimize representational error coming from another direction / domain.
That's fair. Our brains and attentions are finite, you always have to limit the scope. If you imagine you'd have practically forever, you could sort it out and make it all consistent to arbitrary degree (subject to fundamental computational limits, which are physical limits). In practice, the heuristic of consistency works like this:
- For things within your domain of interest, inconsistent information flags an error.
- For things at the interface between your domain of interest and another domain(s), inconsistent information flags an abstraction boundary. It's where you can observe simplifications both domains make because they don't add up (and if you adjust them to make them mutually consistent, you just allowed two domains to work together).
Yes. Fortunately, we also usually don't need the error to be zero. In practice, we usually have narrow scope at any given time, and can get away with a lot of error.
E.g. people in the past found alternatives to modern germ theory, involving evil spirits and other such shenanigans, but to the extend they covered the high-level mechanisms (curse transfers through contact, hygiene and boiling water removes the harmful effects, etc.), it doesn't really matter the theories were wrong. The beliefs were consistent with each other and empirical evidence to some degree, and to that degree were useful.
> And a theory focusing on one aspect, minimizing representational error from one direction of approaching it, necessarily has to make assumptions that will contradict those made by another theory trying to minimize representational error coming from another direction / domain.
That's fair. Our brains and attentions are finite, you always have to limit the scope. If you imagine you'd have practically forever, you could sort it out and make it all consistent to arbitrary degree (subject to fundamental computational limits, which are physical limits). In practice, the heuristic of consistency works like this:
- For things within your domain of interest, inconsistent information flags an error.
- For things at the interface between your domain of interest and another domain(s), inconsistent information flags an abstraction boundary. It's where you can observe simplifications both domains make because they don't add up (and if you adjust them to make them mutually consistent, you just allowed two domains to work together).